Sunday, October 22, 2006

Dark Matter

This of course justifies uninhibited shopping in every brain downtime. For instance yesterday, I heard a talk by Sean Carroll, after which I was so confused about the direction of time that I went to get some chocolate as antidote. And that's how I found a model of the universe. It came in a bar of aero chocolate, one of the numerous children from the Nestlé family. It basically consists of:

An high amount of emptiness which puffs up the volume. As I learned from Wikipedia, exactly how this works is one of the best kept secrets on earth. ( "The exact procedure [...] is a closely guarded secret. A spokesperson for Nestlé provided some clues but there has been no definitive answer." )

Since it's a Nestlé product, the actual solid part of the bar consists of an almost negligible amount of the real thing (that is in this case cacao), which leads us to the conclusion that...

... the rest is a pretty mysterious dark matter, which (ALLERGY ALERT) might contain traces of this or that.

73% of the universe's content is dark energy, responsible for the observed accelerated expansion, exactly how this works is one of the best kept secrets of the universe ("A spokesperson from Super Zing-Zong provided some clues...")

Only 4% is baryonic matter, or the real thing that we are made of...

... and 23% is non-baryonic dark matter, a mysterious but apparently unavoidable ingredient which makes out a disturbingly high fraction of the matter content.

On Wednesday we had a very interesting colloquium by Stefan Hofmann about the small scale structure of dark matter. It was one of these talks that succeed to capture the fascination of understanding a part of how the universe works, a talk that reminded me why I studied physics - and convinced me that the end of physics is nowhere close by.

Stars and other objects that are bound to spiral galaxies rotate around a common center. The rotation velocity of the stars is such that the orbits are stable. The required velocity for this depends on the attractive force acting on the star, which results from the matter content in the galaxy. The larger the force, the higher the velocity has to be to allow for a stable orbit.

Measuring the velocities of stars as a function of their distance to the galaxy's center therefore allows to draw conclusions about the matter distribution inside the galaxy. As it turns out, the visible amount of matter is not remotely sufficient to explain the observations, which in the outer regions of galaxies show larger velocities than expected (its square remains constant instead of dropping inverse to the distance). The observations can be explained by assuming a significant amount of non-visible (dark) matter which is distributed in the galaxy.

The challenge here is that the ratio of dark matter to visible matter (the mass-to-light ratio, commonly denoted M/L) depends on the type of galaxy. E.g. globular clusters show little or no evidence for dark energy.

b) Virilization of Galaxy Clusters

In a similar way, clusters of galaxies have a dynamics that is related to the total mass of the cluster, a relation which can be estimated using the virial theorem. Again, one finds that the visible matter is not remotely sufficient to explain the observations. Measurements indicate a mass-to-light ratio of M/L~300. Though there is some uncertainty as to whether clusters of galaxies have had sufficient time to properly virialize their internal motion, this evidence is pretty strong.

c) Weak Gravitational Lensing

General Relativity predicts that travelling light is bent by mass distributions. If a large amount of mass lies between us and objects that we are looking at, the image of the object can be noticeably distorted. This is known as gravitational lensing.

If the light bending is strong, it can result in multiple images of the source (examples here), or change a point-like shape into arcs. In case the bending is not strong enough to actually produce multiple images, as is typically the case when the matter that causes it is not cleanly localized, one can still measure resulting fuzzy distortions of the background image. In this case, which is known as weak gravitational lensing, the significance for the observed effect has to be enhanced by accumulating sufficient statistics.

Dark matter, though not visible on its own, causes gravitational lensing as every other stuff. In this way, gravitational lensing provides evidence for Dark Matter, which has been reported e.g. by the Canada-France-Hawaii Telescope:

"Using a series of deep images obtained at the Canada-France-Hawaii Telescope over the past two years, the French team analyzed the shapes of some 200,000 faint galaxies spread over two square degrees of the sky (an area approximately 10 times greater than that of the full moon). They have determined that the galaxies appear to be elongated in a coherent manner over large regions of the sky. The measured effect is small, a percent or so deviation from a purely random distribution of shapes, but the accuracy of the results leaves no doubt that the signal is due to the gravitational lensing effect of the dark matter distribution. These results have been partially confirmed by subsequent reports from two teams, one English and the other American, who have studied different patches of the sky."

The stuff that builds up everything we sit on, live from, and can order at amazon.com fails disastrously when it comes to explain what we see at the night sky. Ordinary matter, also called 'baryonic matter', just doesn't clump enough during the evolution of the universe. To be more precise, it does not clump on small enough scales. To explain the observed density contrast and fluctuations, it requires a non-baryonic type of matter (non-baryonic meaning it is not something from the standard model of particle physics, or a synonym for we-don't-know-what). Moreover, this type of matter has to be rather cold, otherwise its temperature also wouldn't allow sufficient clumping. So, what we really need is non-baryonic cold dark matter (CDM).

The best evidence for this comes from the WMAP data, where the third peak in the distribution of temperature fluctuations (Delta T, the vertical axis) over angular momenta (l, the horizontal axis) is the indicator for a large fraction of dark matter. This is very nicely to see in the animation below (borrowed from this website). It shows how the peaks in the WMAP data change with turning up and down the fraction of CDM, denoted with Omega_m, displayed in the pink bar on the right.

The model we use to describe the universe on large scales is classical General Relativity (GR), its ingredients being the background metric which describes space-time, and source terms from the matter that cause the background to be curved. There are then basically two ways to explain the above deviations from this model: either our understanding of GR or that of the sources is incomplete.

The first possibility sounds tempting at first but faces severe challenges. GR on distances of the solar system is extremely well confirmed, so any modification could only set in at larger distances. A modification becoming important at a fixed distance however could never explain the observed rotation velocities for spiral galaxies, whose constant asymptotic value depends on the luminosity of the galaxy, a relation which is known as the Tully-Fisher relation.

This then leaves us with the second possibility of finding source terms with the right properties to explain the observations. Candidates that fulfill the requirements for CDM luckily appear more or less naturally in various extensions of the standard model. These candidates can be characterized as a) being weakly interacting (via gravity and weak interactions only) with each other as well as with baryonic matter and b) being more massive than the common particles of the standard model. Both points are necessary for a sufficient clumpiness as well as to explain why we haven't yet seen these particles.

The problem with the above mentioned CDM candidates is that their exact nature doesn't play a role for the observed rotation curves or the large scale structure. Though these particle differ in their microscopic properties, these have no imprint on the above mentioned observations. The present concordance model of cosmology (Lambda-CDM) is basically a parametrization of our ignorance about the nature of the universe's ingredients.

There are ways to examine the nature of CDM directly. There is of course the possibility that the WIMPs will be found in high energy experiments on earth if the collision energy exceeds the necessary production energy. And even though the WIMPs are weakly interacting, it still happens every now and then that they do interact. Decay products of such reactions can in principle be detected. The neutralino for example, is its own anti-particle, and it can annihilate into photons. The probability for this to happen depends on the density of the CDM (the rate is proportional to the squared density) and is typically very low. This makes experiments a very challenging task: The expected flux of photons on earth is approximately the same 'as we would receive from a single candle placed on Pluto' (source: astro-ph/0501589).For more details about experiments on direct detection, see e.g.

But here's the point: each point in this simulation corresponds to 106 solar masses. All smaller structures are not resolved. What Stefan Hofmann and collaborators showed in their work though was that CDM's smallest structures are 12 orders of magnitude smaller than that! This applies generally for those types of CDM that have been in thermal and chemical equilibrium with the radiation in the early universe. This is typically the case for neutralinos and binos, but not for axions, in which case the small scale structure would look differently (he says work is in progress).

Starting with a primordial initial power spectrum, they calculated the evolution of this spectrum, for the first time including collisional damping and free-streaming. As Stefan said in his talk, in principle there is a third contribution from heat conduction 'but heat is a pretty boring thing for cold stuff, so we drop this term'. In their work they showed that the spectrum has a sharp cut-off at about 10-6 solar masses, below which there are no smaller substructures. You find a very readable summary on the arxiv

Cosmologists measure time in redshift, commonly denoted with z. We are today at z=0. The larger z, the further in the past an event was. Hofmann's analytical calculations hold down to z approximately 60, where the linear perturbation theory can no longer be applied because the density contrast has become too large. These analytical results however, can then be used as input for numerical calculations. This has been reported in a Nature article

where the numerical calculation goes down to approximately z=20. Results of this simulation are shown in the picture below, where the small structures are magnified

(If you have no access to Nature, the same article is also available at astro-ph/0501589)

These smallest CDM halos without further substructure are distributed over a size of roughly the solar system, which means they are extremely diluted. Their average velocity is approximately 1 meter per second. They are estimated to propagate through galaxies without being disrupted, which means that these CDM substructures could travel through our solar system and render the background we live in time-dependent!

To summarize: the microscopic nature of CDM has an imprint on the small scale structure of our universe. The examination of these small scale fluctuations therefore would allow us to distinguish between different candidates for CDM.

Audio, Slides and Video of Stefan Hofmann's talk: Go to Perimeter's Streaming Seminars, click on 'Seminar Series' on the left side, in the field 'Find presentations' type 'Missing Link' and click on the search button (they are working on an improvement..., no honestly, I have seen the upcoming new sites with my own eyes!)

"[...] a kind of intermediate state in which all that is missing to make it practical knowledge is a mathematically sound microscopic realization."

Well, yes, that is ' all ' that is missing ;-)

But as a theoretical physicist in the 21st century, I have to give credits to the experimental achievements. We have plenty of evidence for physics beyond the standard model. Astrophysics and cosmology provide us with numerous puzzles to keep our days busy. In case someone got the impression, we theoretical physicists are not sitting around being depressed about the trouble with physics. We just don't have the time! The universe is waiting to be explored. And if you aren't yet convinced of the beauty of it all, go get some chocolate.

which simulation code? I guess, the millenium thing wouldn't be of much use unless you have computer cluster in your basement ;-) (In which case the FBI would probably be interested to hear.)

Regarding Tully-Fisher: the simulation does not go down to z=0 and therefore not to present day galaxy structures. Everything below z approximately 20 is an estimation (see e.g. the mentioned Nature article). Furthermore, the simulation doesn't include baryonic matter, so it doesn't say anything about Tully-Fisher, which needs the M/L. Best,

1. Pointing the high gain antenna at earth obtains perhaps a factor of 100 in power received. Being twice as far away as Pluto reduces it by a factor of 4; so we can "detect a 200 W bulb on Pluto". Maybe better, because the reason Pioneer went silent is because its power generators degraded, not because it was too distant.

I think the problem might be more to decide which band of the spectrum to look in, and to get the detector far out enough into space to reduce interference. Do we know where to look perhaps is the question.

sure. I said it's challenging, not it's impossible. I have seen 'photos' of galaxies, consisting of only 11 photons or so!

Do we know where to look perhaps is the question.

You would want to look somewhere where the CDM density is high, like the center of our galaxy. Which frequency band to look in is promising should follow from the differential cross-section for the annihilation process to happen. Best,

Interesting stuff, but I theoretical interpretation can mean everything here, and regardless of whatever odds against my being correct, I still don't think that GR need be modified if the vacuum is comprised of rarefied mass energy, where the density of the *finite* vacuum is -0.5*rho(matter) because, rho+3P/c^2=0.

Pressure is negative in an expanding universe, and so energy density is positive, i.e., The vacuum energy density is less than the matter energy density, but it is still positive and will naturally tend to condense gravitationally around massive clusters in a less dense form even than virtual particles, so much of the matter interacts with photons more weakly than the known forces that couple light interactions to baryonic matter, while acting as a compactor of structure.

Hi Island, well yeah, you don't need to modify GR if you include a funny source term with strange properties to explain the observed expansion of the universe. Whether you call that quintessence, vacuum energy, anti-gravitation or comprised of rarefied mass energy (whatever that's supposed to mean) doesn't make a big difference. You write it down, it has an equation of state, you plug it into GR. That either fits to experimental facts, or it doesn't. But then you still haven't explained the micro-physics of the stuff you've plugged in. Best, B.

Aaron Bergman said... Surely weak lensing should be included on the list of evidence for dark matter.

Ah, right! It got lost somewhere on the way from drafting to writing down (Blogger was down pretty much of yesterday evening and I lost several parts of what I wrote, very annoying). I didn't mean to discriminate weak lensing ;-) I will add it to the list if I find the time...

include a funny source term with strange properties to explain the observed expansion of the universe

Not necessary Bee, because you have to condense the rarefied energy to attain the matter density before Feynman takes over and that causes further rarefaction which increases negative pressure in a finite vacuum, therby driving expansion without need for mysterious outside interference. That means that it requires a greater volume of vaccum energy each time that you make a particle pair or a virtual particle, and that causes expansion to accelerate.

I've never found a problem that this doesn't resolve, including the flatness problem, since the increase in the matter density is offset by the increase in negative pressure, so this *necessarily* holds the vacuum stable and flat as it expands at an accelerating rate.

That's what happens as soon as you start generating matter from a zero pressure, G=0 metric.

In this case, G=0 when there is no matter density, the only way to get rho>0 out of Einstein's matter-less model is to condense the matter density from the existing structure, and in doing so the pressure of the vacuum necessarily becomes less than zero, P, less than 0.

I don't get it. What do you mean with G=0 ? The trace of the Einstein tensor vanishes? This implies \rho = 3p, not vanishing \rho? Sorry, I am kind of confused here.

Hi Rob,

Thanks for noticing that the post above is *not* about dark energy, but actually about the small scale structure of cold dark matter.

Yes, I thought repeatedly about writing a piece on the cosmological constant, but the problem (besides the usual problem with time) is that I can't make up my mind which explanation I favour. Current status is that I think Lambda vanishes, and everything else is an interpretational bug (the reason being that I noticed yesterday I made a mistake thinking I made a mistake with the anti-gravitation, but enough...!).

But yes, I promise herewith that I will write a post about the cosmological constant problem. It will be a seriously biased one though.

Hi Bee, I'll try to be a clear as I can, and please take in the whole point here, as well:

The graviational acceleraton is zero if the density of the static vacuum is -0.5*rho(matter) because, rho+3P/c^2=0.

If you condense enough energy over a finite region of space to achieve postive matter-density, then the local increase in positive gravitaional curvature is immediately offset by the increase in negative pressure that occurs via the rarefying effect that real particle creation has on the vacuum.

That means that created particles have positive mass, regardless of sign, and this resolves a very important failure of particle theory, becuase it explains how and why there is no contradiction with the asymmetry that appears to exist between matter and antimatter. This is the reason that we don't observe nearly as much antimatter as particle theory predicts exists, because the energy that comprises the observed antimatter particles normally exists in a more rarefied state than observed antiparticles do.

The vacuum expands slowly, over time, while the universe is held nearly flat and stable, because tension between ordinary matter and the vacuum increases. The "flexible rubber sheet analogy would be to stick a fork into the zero pressure metric and spin. Note that the rubber sheet pulls back with increasing negative pressure.

It is made apparent that a negative energy wave is a gravitational wave that has a positive energy density but negative pressure, so that the wave density is smaller than the matter energy density, (but still positive), having a gravitational effect of positive energy density that's just outweighed by the gravitaional repulsion of negative vacuum pressure.

So, g=(4pi/3)G(rho(matter)-2rho(vacuum))R=0

When I say that this never fails to resolve the problems, I'm talking mostly about the anthropic problems, and causality, because growing tension between the vacuum and ordinary matter will inevitably eventually compromise the integrity of the forces that compromise this finite structure, and BOOM!... ;)... there is no horizon problem, and no need for inflationary band-aids to big bang theory when a universe with certain volume has a big bang.

Ectceteras...

Monopoles... won't be expected... for example.

These asymmetric transitions that occur with matter generation from **negative** vacuum energy represent the literal connection to the anthropic principle, while defining the mechanism that enables the universe to "leap" without EVER violating the second law.

yes, sure, there are collider constraints on the existence of dark matter candidates as well. See eg. the Particle Data Booklet (the new life-sites are pretty cool!), constraints on Neutralinos and Axions. Thus, yes you could say that we would produce these things in the collider should they exist. But their lifespan better be not extremely short, otherwise they would make a pretty bad CDM candidate. The neutralino e.g. would be the LSP, and be protected from decay.

a very interesting post :-), and I always wanted to know a little bit about Stefan's work on cold dark matterand structure formation.

So, the concentrations of CDM Stefan has investigated correspond to roughly the mass of the Earth, which is about 3x10e-6 solar masses, distributed over the volume of the whole solar system? Did I get that right?

If I use for simplicity 40 AU's or 6x10e9 km for the radius of the solar system, this volume is about 10e18 the volume of Earth.

Is that correct? But then, the density of the CDM concetration is tiny, indeed! Is it not even smaller than the average density of dust etc. in the solar system? Confusing...

yes, that's about correct, though I think the mass of the smallest halos is closer by mass of Mars than of Earth (I dropped some factors of order one). That makes a very thin medium if it travels through our solar system, indeed.

I am not sure but maybe one would be able to find traces of the time-dependence? I mean, given that such an event would happen with non-negligible probability, would it affect the motions of planets? Asteroids? I mean, if a tiny mass like that of non-planet Pluto can be predicted from it's influence on other orbiting objects, then maybe a Mars-mass CDM halo would influence the orbit of Pluto?

Thanks for your explanation, which is very helpful indeed. I have some questions though.

1) What do you do with ultrarelativistic matter?

2) Where goes Baryogenisis?

3) If you keep spacetime flat by producing pairs via the mechanism you described, how come spacetime isn't flat? What you propose would not only affect Cosmology but also astrophysics. Why does the apple fall down?

4) Why is your rarefied stuff stable and doesn't decay into more and more negative energy states?

5) If I get that right you are basically trying to stabilize Einstein's static universe by conjecturing some quantum effects whose nature you don't explain (you neither compute a particle creation rate, nor do you give any reason why your negative energetic field doesn't decay). But besides this, the static universe isn't in agreement with observations.

Hi Sabine, great post!I quite like aeroes even if they have low (the real thing) cacao content, and the holes are produced by a guarded secret and allergy causing additives. To date I have not encountered any allergies to food additives. lol!Mint aeroes are a little bit over the top, like menthol cigarrettes.But have you thought of a giant honeycombed malteser wrapped in thick chocolate - hmmm - so light too. Not that weight appears to be a problem for you.

glad you liked my post :-) I find the topics dark matter and dark energy as annoying as fascinating. One way or the other, for the theoretician it's a huge challenge, and admittedly kind of addictive. Over the last years (since WMAP or so), I've talked to so many colleagues, and almost everybody has his/hers interpretation of how to explain the observations, many of which are working on pinning down their ideas. I expect there will be happening a lot the next years.

I sometimes wonder how I ended up being a particle physicist, as it seems to be much more in my nature to stare into the distance, trying to get the large picture, than taking things into pieces and examining the microscopic details...

I don't find the bubble-bars bad at all, but as with so many things in life I guess it's a matter of what you expect. If you expect chocolate, it's a disappointment. But regarding the chocolate, Nestle is still better than Hershey's. If I can, I go for Lindt, which at least manages to reproduce the chocolate feeling. I haven't tried the aeros with mint, but those with caramel are also nice :-)

If the reversal of Time is applied to the Aero chocolate bar, then it starts of as a Liquid, the bubbles are introduced, Airated?..then left to solidify.

Heat causes the naturally "cold" solid chocolate to "melt".

One can state that a chololate Universe is initially "cold_solid" ,then heats up to boiling liquid point "bubbled" ,then cools back down to a stable solid temperature, then distributed as Bars of Galaxy,maybe?

A quick disclaimer - I don't disbelieve the astronomers. I just want to understand how they do their observations.

A long ago, when first the He/H ratio of the primordial universe was a marker of how many generations of particles we had, I ventured to read a astronomer's article on a measurement of this all-important ratio. Sorry, I won't be able to find the reference without a great search. This is what I remember after all those years.

The astronomers measured the He/H ratio in a bunch of stars chosen because the nuclear reprocessing would be the least. The He/H ratio showed a healthy scatter in the sample of stars. They tried to correlate the He/H ratio to the metallicity, the idea being that the He/H ratio and the metallicity would correlate neatly, and they could extrapolate neatly to zero metallicity to get the primordial He/H ratio. Unfortunately that idea did not work. So, finally, they took the average of their sample, and proclaimed that to be the primordial He/H ratio. Of course, it was the value consistent with 3 generations.

To me, not addressed there was that (if there are not He/H segregation processes going on in stellar atmospheres)

1. they were only measuring an upper bound on primordial He/H.

2. if their metallicity test had worked, they'd have extrapolated down to zero metallicity. But even if it didn't work, doesn't the **lowest** He/H ratio measured put the upper bound on primordial He/H?

3. what errors were they minimizing by averaging over their sample?

I came away from that reading with a disappointment. It was only one small individual point in the overall result, and I don't have serious doubts about the result. But theoretical papers would point to the abstract as though an observationally final and complete answer had been found. Possible loopholes are in the details.

I recently look in my (outdated by now, I'm sure) Galactic Astronomy by Binney and Merrifield. Galactic rotation curves outside the optical limits of the galaxy depend on HI emissions. B&M do say that most of the HI in the disks of spiral galaxies follow approximately circular orbits. But there is something remaining to be explained as well: HI distribution is lopsided. "Since the period of rotation of a gas cloud is roughly proportional to its galactocentric distance, in a few rotation periods ~ I Gyr, differential rotation should smear an initially lopsided distribution of gas into an axisymmetric distribution. Hence it is surprising that lop-sided distributions of HI are common.........There is no generally accepted explanation of why lop-sidedness is so common given the comparatively short lifetime of an initially lop-sided distribution mentioned above".

Doesn't mean that the rotation curves are wrong, just a reminder of the fact that we don't understand the dynamics of the HI clouds very well, it would seem.

Also, I don't know if intimate acquaintance with the details stimulates the theoretical imagination (by removing supposedly hard constraints) or inhibits it (by overwhelming it with detail).

Thanks for your comments. You are right that in many cases the so-called experimental evidence is much more involved than it appears at first sight. There are many factors and assumptions that often aren't explicitly pointed out. Your concern might be one, but one way or the other there would be something left open to explain.

In the case of dark matter the evidence seems to be just overwhelming. Whether or not the postulation of dark matter solves all of the above mentioned puzzles (and yours in addition) is an open question. I personally doubt it.

I also admit that as a theorist it has repeatedly annoyed me how badly many experimental groups document their data analysis (global neutrino fits are an especially severe case).

Regarding your question how they got the details around 30 arcsec, I don't know. I would guess they were just lucky to have many visible objects there. However, I miss some errorbars in this figure. It's not clear to me whether the 'detail' isn't actually just a statistical fluctuation or something.

“And isn't that a nice way to model our universe, where the present day cosmological data lets us conclude that.…23% [of the universe] is non-baryonic dark matter….”, The foundation of the model that Bee is marveling about has an unflattering similarity to the foundation of the model of the universe that Scholastics extolled. No one then and now has been able to come with a viable reason why all objects in the sky revolve around the earth in a 24-hour period? Similarity no one yet, despite Newton’s prompting, has been able to come up with a scientific reason why mass can either can attract other mass or warp space. With this similarity between the two cherished models and the fact that 95 % of the supposed constituents of the universe cannot be detected in the laboratory, I would think our theorists today would want to follow the example set by Copernicus and Darwin and build a gravity theory based on an independent foundation that could at least be further understood. But in reality, I know it is unrealistic to expect such a learned body to carry out this essential step. I realize that they are over trained and cannot as the saying goes “see the forest for the trees.”Well aware of this blinding effect or formal graduate training in a discipline, 30 years ago, when the need for the dark matter appeared on the scene, I set about to build a gravity theory on a new foundation that met the criteria of being further interpretable.So I hope that there is at least some skepticism about “our present model of the universe” for some readers of this blog to at least look at the result of my “years in the attic.” Check out my experiments establishing the validity of my basic assumption. Find out what I mean by the “3-D lever that exists in every star” from which Newton’s Law of Universal Gravitation can be derived. See how I use the literal interpretation of the Tully Fisher law, as well as the bending of light found within a galaxy, to explain the flat rotation curves of galaxies. Finally, see how the coincidence between the dimming of the universe and its acceleration can provide a way to make the dark energy superfluous. All you have to do is to take ten minutes of your time and go to my blog athttp://infralever.blogspot.com/

All this so-called evidence of dark matter is not so solid as is often claimed.

1) Galaxy rotation curves:

These do not demonstrate the presence of dark matter. They show that the stars do not follow Newton's law of gravitation. Newton's law has been obtained by observations on a very small scale (our solar system) and it is no surprise that it breaks down when extrapolating the scale by a factor 1E6 to 1E12 (or more).

2) Virial theorem applied to cluster of galaxies

Again, it only shows that Newton's law is not consistent with the observations

3) gravitational lensing

These observations only shows that GR is not able to describe light bending over very large scales. Light bending around our sun has been described correctly by GR but again here the scale is much smaller than galactic scales. Since GR has been made to coincide to Newton's theory in the nonrelativistic limit, it is clear that when one Newton's law is not correct at large distances, that GR will also not be correct at large distances

4) WMAP data

Here the interpretation depends on a cosmological model which could be very wrong. For instance, the assumption that the universe is homogeneous on large scales seems not to be correct as one recently has observed extremely large voids. These models depend on so many assumptions (such as on inflation) that any conclusions derived from them are highly questionable.

So, in the end, all "evidence" melts away and one is left with the sober fact that not one single dark matter particle has been observed.

Luckily, there are alternatives to dark matter. Several of them can be found on the Arxiv website (such as http://arxiv.org/abs/0712.1110 ) and several of these have been published in peer reviewed journals.

; if dark matter is confirmed by gravitiation lensing, wha t is the effect of angular momentum of planets and sars on gravitional lensing and has this been taken into account. how fo we measure mass of objects diatance from us; estimates of mass and planets, and dust, and angular mementum is sure to add up to more then our estimates based on stars (visable matter alone) how is all this accounted for before we chuck it up to a mysterious dark matter???

Anonymous,There is a long history in which people have tried to explain dark matter with unseen planets, brown dwarfs, or even black holes - i.e. non-luminous but 'normal' matter. One can estimate these contributions by looking at the distribution of such components in our own Galaxy. There is no way they can contribute as much as than ten times more than the visible mass. Besides this, experiments show that dark matter does not clump the same way as usual matter does, it interacts either weakly or only gravitationally. The Bullet cluster measurements show this very nicely. Best,

All this can also be explained by assuming that General Relativity is wrong by a factor 10 (when it comes to light bending). Dark matter has been attributed many strange properties and I would like to add another one: high intelligence! This dark matter has to move and clump in exactly the right way to make the galaxy rotation curves flat. In addition, it constantly find tricks to evade detection in particle accelerators. Sometimes however, it makes a mistake such that one can observe galaxies without dark matter (see http://space.newscientist.com/article/dn13280-galaxy-without-dark-matter-puzzles-astronomers.html as well as some other examples) ...

I was just thinking just yesterday and before I found this excellent page that neutrinos may be the best candidates for Dark Matter among particles that are already known, party because stars have a way of producing quite a bit of them.

Then with a few mouse clicks (research) I found there's something called sterile neutrinos, and then this page mentions heavy sterile neutrinos. How do they become sterilized and then heavy? Darn if they aren't the most seriously strange fermions.

One the great discoveries of our lives is that in the short space (by astronomical standards) they travel from sun to earth they vary in mass by oscillating between the 3 generations.

Bee, you've written a paper on neutrino oscillations, what's the latest on that?

I'd comment that Dark Energy is probably simpler yet and has something to do with geometry in one large extra dimension (I see you wrote a paper on large extra dimension(s) too, Bee) but this is a page on Dark Matter only so that's enough for now, thanks.